src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Fri May 27 10:30:07 2011 +0200 (2011-05-27)
changeset 42998 1c80902d0456
parent 42994 fe291ab75eb5
child 43000 bd424c3dde46
permissions -rw-r--r--
fully support all type system encodings in typed formats (TFF, THF)
blanchet@40114
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
blanchet@38282
     2
    Author:     Fabian Immler, TU Muenchen
blanchet@38282
     3
    Author:     Makarius
blanchet@38282
     4
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@38282
     5
blanchet@39494
     6
Translation of HOL to FOL for Sledgehammer.
blanchet@38282
     7
*)
blanchet@38282
     8
blanchet@40068
     9
signature SLEDGEHAMMER_ATP_TRANSLATE =
blanchet@38282
    10
sig
blanchet@42227
    11
  type 'a fo_term = 'a ATP_Problem.fo_term
blanchet@42939
    12
  type format = ATP_Problem.format
blanchet@42709
    13
  type formula_kind = ATP_Problem.formula_kind
blanchet@38282
    14
  type 'a problem = 'a ATP_Problem.problem
blanchet@42640
    15
  type locality = Sledgehammer_Filter.locality
blanchet@42613
    16
blanchet@42613
    17
  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
    18
  datatype type_level =
blanchet@42613
    19
    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@42837
    20
  datatype type_heaviness = Heavy | Light
blanchet@42613
    21
blanchet@42613
    22
  datatype type_system =
blanchet@42722
    23
    Simple_Types of type_level |
blanchet@42837
    24
    Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
    25
    Tags of polymorphism * type_level * type_heaviness
blanchet@42613
    26
blanchet@40114
    27
  type translated_formula
blanchet@38282
    28
blanchet@42646
    29
  val readable_names : bool Config.T
blanchet@40204
    30
  val fact_prefix : string
blanchet@38282
    31
  val conjecture_prefix : string
blanchet@42881
    32
  val helper_prefix : string
blanchet@42881
    33
  val typed_helper_suffix : string
blanchet@42966
    34
  val predicator_name : string
blanchet@42966
    35
  val app_op_name : string
blanchet@42966
    36
  val type_pred_name : string
blanchet@42962
    37
  val simple_type_prefix : string
blanchet@42613
    38
  val type_sys_from_string : string -> type_system
blanchet@42613
    39
  val polymorphism_of_type_sys : type_system -> polymorphism
blanchet@42613
    40
  val level_of_type_sys : type_system -> type_level
blanchet@42613
    41
  val is_type_sys_virtually_sound : type_system -> bool
blanchet@42613
    42
  val is_type_sys_fairly_sound : type_system -> bool
blanchet@42542
    43
  val unmangled_const : string -> string * string fo_term list
blanchet@41088
    44
  val translate_atp_fact :
blanchet@42994
    45
    Proof.context -> format -> type_system -> bool -> (string * locality) * thm
blanchet@42640
    46
    -> translated_formula option * ((string * locality) * thm)
blanchet@40059
    47
  val prepare_atp_problem :
blanchet@42939
    48
    Proof.context -> format -> formula_kind -> formula_kind -> type_system
blanchet@42939
    49
    -> bool -> term list -> term
blanchet@41091
    50
    -> (translated_formula option * ((string * 'a) * thm)) list
blanchet@42541
    51
    -> string problem * string Symtab.table * int * int
blanchet@42881
    52
       * (string * 'a) list vector * int list * int Symtab.table
blanchet@41313
    53
  val atp_problem_weights : string problem -> (string * real) list
blanchet@38282
    54
end;
blanchet@38282
    55
blanchet@41140
    56
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
blanchet@38282
    57
struct
blanchet@38282
    58
blanchet@38282
    59
open ATP_Problem
blanchet@39494
    60
open Metis_Translate
blanchet@38282
    61
open Sledgehammer_Util
blanchet@42640
    62
open Sledgehammer_Filter
blanchet@42640
    63
blanchet@42640
    64
(* experimental *)
blanchet@42640
    65
val generate_useful_info = false
blanchet@38282
    66
blanchet@42879
    67
fun useful_isabelle_info s =
blanchet@42879
    68
  if generate_useful_info then
blanchet@42879
    69
    SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42879
    70
  else
blanchet@42879
    71
    NONE
blanchet@42879
    72
blanchet@42879
    73
val intro_info = useful_isabelle_info "intro"
blanchet@42879
    74
val elim_info = useful_isabelle_info "elim"
blanchet@42879
    75
val simp_info = useful_isabelle_info "simp"
blanchet@42879
    76
blanchet@42568
    77
(* Readable names are often much shorter, especially if types are mangled in
blanchet@42589
    78
   names. Also, the logic for generating legal SNARK sort names is only
blanchet@42589
    79
   implemented for readable names. Finally, readable names are, well, more
blanchet@42589
    80
   readable. For these reason, they are enabled by default. *)
blanchet@42646
    81
val readable_names =
blanchet@42646
    82
  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
blanchet@42568
    83
blanchet@42998
    84
val type_decl_prefix = "ty_"
blanchet@42998
    85
val sym_decl_prefix = "sy_"
blanchet@42998
    86
val sym_formula_prefix = "sym_"
blanchet@40204
    87
val fact_prefix = "fact_"
blanchet@38282
    88
val conjecture_prefix = "conj_"
blanchet@38282
    89
val helper_prefix = "help_"
blanchet@42543
    90
val class_rel_clause_prefix = "crel_";
blanchet@38282
    91
val arity_clause_prefix = "arity_"
blanchet@39975
    92
val tfree_prefix = "tfree_"
blanchet@38282
    93
blanchet@42881
    94
val typed_helper_suffix = "_T"
blanchet@42881
    95
val untyped_helper_suffix = "_U"
blanchet@42881
    96
blanchet@42966
    97
val predicator_name = "hBOOL"
blanchet@42966
    98
val app_op_name = "hAPP"
blanchet@42966
    99
val type_pred_name = "is"
blanchet@42962
   100
val simple_type_prefix = "ty_"
blanchet@42531
   101
blanchet@42962
   102
fun make_simple_type s =
blanchet@42994
   103
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@42994
   104
     s = tptp_individual_type then
blanchet@42994
   105
    s
blanchet@42994
   106
  else
blanchet@42994
   107
    simple_type_prefix ^ ascii_of s
blanchet@42531
   108
blanchet@38282
   109
(* Freshness almost guaranteed! *)
blanchet@38282
   110
val sledgehammer_weak_prefix = "Sledgehammer:"
blanchet@38282
   111
blanchet@42613
   112
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
   113
datatype type_level =
blanchet@42613
   114
  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@42837
   115
datatype type_heaviness = Heavy | Light
blanchet@42613
   116
blanchet@42613
   117
datatype type_system =
blanchet@42722
   118
  Simple_Types of type_level |
blanchet@42837
   119
  Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
   120
  Tags of polymorphism * type_level * type_heaviness
blanchet@42613
   121
blanchet@42689
   122
fun try_unsuffixes ss s =
blanchet@42689
   123
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   124
blanchet@42613
   125
fun type_sys_from_string s =
blanchet@42722
   126
  (case try (unprefix "poly_") s of
blanchet@42722
   127
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   128
   | NONE =>
blanchet@42613
   129
     case try (unprefix "mono_") s of
blanchet@42722
   130
       SOME s => (SOME Monomorphic, s)
blanchet@42722
   131
     | NONE =>
blanchet@42722
   132
       case try (unprefix "mangled_") s of
blanchet@42722
   133
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   134
       | NONE => (NONE, s))
blanchet@42613
   135
  ||> (fn s =>
blanchet@42689
   136
          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
blanchet@42689
   137
          case try_unsuffixes ["?", "_query"] s of
blanchet@42613
   138
            SOME s => (Nonmonotonic_Types, s)
blanchet@42613
   139
          | NONE =>
blanchet@42689
   140
            case try_unsuffixes ["!", "_bang"] s of
blanchet@42613
   141
              SOME s => (Finite_Types, s)
blanchet@42613
   142
            | NONE => (All_Types, s))
blanchet@42828
   143
  ||> apsnd (fn s =>
blanchet@42837
   144
                case try (unsuffix "_heavy") s of
blanchet@42854
   145
                  SOME s => (Heavy, s)
blanchet@42854
   146
                | NONE => (Light, s))
blanchet@42837
   147
  |> (fn (poly, (level, (heaviness, core))) =>
blanchet@42837
   148
         case (core, (poly, level, heaviness)) of
blanchet@42855
   149
           ("simple", (NONE, _, Light)) => Simple_Types level
blanchet@42854
   150
         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
blanchet@42851
   151
         | ("tags", (SOME Polymorphic, All_Types, _)) =>
blanchet@42854
   152
           Tags (Polymorphic, All_Types, heaviness)
blanchet@42886
   153
         | ("tags", (SOME Polymorphic, _, _)) =>
blanchet@42886
   154
           (* The actual light encoding is very unsound. *)
blanchet@42886
   155
           Tags (Polymorphic, level, Heavy)
blanchet@42854
   156
         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
blanchet@42854
   157
         | ("args", (SOME poly, All_Types (* naja *), Light)) =>
blanchet@42837
   158
           Preds (poly, Const_Arg_Types, Light)
blanchet@42854
   159
         | ("erased", (NONE, All_Types (* naja *), Light)) =>
blanchet@42837
   160
           Preds (Polymorphic, No_Types, Light)
blanchet@42753
   161
         | _ => raise Same.SAME)
blanchet@42753
   162
  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
blanchet@42613
   163
blanchet@42722
   164
fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
blanchet@42828
   165
  | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
blanchet@42828
   166
  | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
blanchet@42613
   167
blanchet@42722
   168
fun level_of_type_sys (Simple_Types level) = level
blanchet@42828
   169
  | level_of_type_sys (Preds (_, level, _)) = level
blanchet@42828
   170
  | level_of_type_sys (Tags (_, level, _)) = level
blanchet@42828
   171
blanchet@42837
   172
fun heaviness_of_type_sys (Simple_Types _) = Heavy
blanchet@42837
   173
  | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
blanchet@42837
   174
  | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
blanchet@42831
   175
blanchet@42687
   176
fun is_type_level_virtually_sound level =
blanchet@42687
   177
  level = All_Types orelse level = Nonmonotonic_Types
blanchet@42613
   178
val is_type_sys_virtually_sound =
blanchet@42613
   179
  is_type_level_virtually_sound o level_of_type_sys
blanchet@42613
   180
blanchet@42613
   181
fun is_type_level_fairly_sound level =
blanchet@42613
   182
  is_type_level_virtually_sound level orelse level = Finite_Types
blanchet@42613
   183
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
blanchet@42613
   184
blanchet@42994
   185
fun is_setting_higher_order THF (Simple_Types _) = true
blanchet@42994
   186
  | is_setting_higher_order _ _ = false
blanchet@42994
   187
blanchet@40114
   188
type translated_formula =
blanchet@38752
   189
  {name: string,
blanchet@42640
   190
   locality: locality,
blanchet@42525
   191
   kind: formula_kind,
blanchet@42562
   192
   combformula: (name, typ, combterm) formula,
blanchet@42562
   193
   atomic_types: typ list}
blanchet@38282
   194
blanchet@42640
   195
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
blanchet@42640
   196
                          : translated_formula) =
blanchet@42640
   197
  {name = name, locality = locality, kind = kind, combformula = f combformula,
blanchet@42562
   198
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   199
blanchet@42558
   200
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
blanchet@42558
   201
blanchet@42677
   202
blanchet@42753
   203
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   204
datatype type_arg_policy =
blanchet@42753
   205
  Explicit_Type_Args of bool |
blanchet@42753
   206
  Mangled_Type_Args of bool |
blanchet@42753
   207
  No_Type_Args
blanchet@41136
   208
blanchet@42836
   209
fun should_drop_arg_type_args (Simple_Types _) =
blanchet@42836
   210
    false (* since TFF doesn't support overloading *)
blanchet@42836
   211
  | should_drop_arg_type_args type_sys =
blanchet@42836
   212
    level_of_type_sys type_sys = All_Types andalso
blanchet@42837
   213
    heaviness_of_type_sys type_sys = Heavy
blanchet@42831
   214
blanchet@42589
   215
fun general_type_arg_policy type_sys =
blanchet@42589
   216
  if level_of_type_sys type_sys = No_Types then
blanchet@42589
   217
    No_Type_Args
blanchet@42589
   218
  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
blanchet@42831
   219
    Mangled_Type_Args (should_drop_arg_type_args type_sys)
blanchet@42589
   220
  else
blanchet@42831
   221
    Explicit_Type_Args (should_drop_arg_type_args type_sys)
blanchet@42563
   222
blanchet@42951
   223
fun type_arg_policy type_sys s =
blanchet@42951
   224
  if s = @{const_name HOL.eq} orelse
blanchet@42966
   225
     (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
blanchet@42951
   226
    No_Type_Args
blanchet@42951
   227
  else
blanchet@42951
   228
    general_type_arg_policy type_sys
blanchet@42227
   229
blanchet@42956
   230
fun atp_type_literals_for_types format type_sys kind Ts =
blanchet@42956
   231
  if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ then
blanchet@42353
   232
    []
blanchet@42353
   233
  else
blanchet@42353
   234
    Ts |> type_literals_for_types
blanchet@42353
   235
       |> filter (fn TyLitVar _ => kind <> Conjecture
blanchet@42353
   236
                   | TyLitFree _ => kind = Conjecture)
blanchet@41137
   237
blanchet@42534
   238
fun mk_aconns c phis =
blanchet@42534
   239
  let val (phis', phi') = split_last phis in
blanchet@42534
   240
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   241
  end
blanchet@38282
   242
fun mk_ahorn [] phi = phi
blanchet@42534
   243
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   244
fun mk_aquant _ [] phi = phi
blanchet@42522
   245
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   246
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   247
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   248
blanchet@42522
   249
fun close_universally atom_vars phi =
blanchet@41145
   250
  let
blanchet@41145
   251
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   252
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   253
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   254
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   255
        union (op =) (atom_vars tm []
blanchet@42526
   256
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   257
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   258
blanchet@42531
   259
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   260
  | combterm_vars (CombConst _) = I
blanchet@42574
   261
  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
blanchet@42674
   262
fun close_combformula_universally phi = close_universally combterm_vars phi
blanchet@42522
   263
blanchet@42522
   264
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42998
   265
  is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
blanchet@42674
   266
fun close_formula_universally phi = close_universally term_vars phi
blanchet@41145
   267
blanchet@42994
   268
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
blanchet@42994
   269
val homo_infinite_type = Type (homo_infinite_type_name, [])
blanchet@42994
   270
blanchet@42994
   271
fun fo_term_from_typ higher_order =
blanchet@42994
   272
  let
blanchet@42994
   273
    fun term (Type (s, Ts)) =
blanchet@42994
   274
      ATerm (case (higher_order, s) of
blanchet@42994
   275
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   276
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@42994
   277
             | _ => if s = homo_infinite_type_name then `I tptp_individual_type
blanchet@42994
   278
                    else `make_fixed_type_const s,
blanchet@42994
   279
             map term Ts)
blanchet@42994
   280
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@42994
   281
    | term (TVar ((x as (s, _)), _)) =
blanchet@42994
   282
      ATerm ((make_schematic_type_var x, s), [])
blanchet@42994
   283
  in term end
blanchet@42562
   284
blanchet@42562
   285
(* This shouldn't clash with anything else. *)
blanchet@42542
   286
val mangled_type_sep = "\000"
blanchet@42542
   287
blanchet@42562
   288
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   289
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   290
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   291
    ^ ")"
blanchet@42542
   292
blanchet@42998
   293
val bool_atype = AType (`I tptp_bool_type)
blanchet@42998
   294
blanchet@42994
   295
fun ho_type_from_fo_term higher_order pred_sym ary =
blanchet@42963
   296
  let
blanchet@42963
   297
    fun to_atype ty =
blanchet@42963
   298
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@42963
   299
              generic_mangled_type_name snd ty))
blanchet@42963
   300
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   301
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   302
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@42994
   303
    fun to_ho (ty as ATerm ((s, _), tys)) =
blanchet@42994
   304
      if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
blanchet@42994
   305
  in if higher_order then to_ho else to_fo ary end
blanchet@42963
   306
blanchet@42994
   307
fun mangled_type higher_order pred_sym ary =
blanchet@42994
   308
  ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
blanchet@42963
   309
blanchet@42994
   310
fun mangled_const_name T_args (s, s') =
blanchet@42963
   311
  let
blanchet@42994
   312
    val ty_args = map (fo_term_from_typ false) T_args
blanchet@42963
   313
    fun type_suffix f g =
blanchet@42963
   314
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   315
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   316
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   317
blanchet@42542
   318
val parse_mangled_ident =
blanchet@42542
   319
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   320
blanchet@42542
   321
fun parse_mangled_type x =
blanchet@42542
   322
  (parse_mangled_ident
blanchet@42542
   323
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   324
                    [] >> ATerm) x
blanchet@42542
   325
and parse_mangled_types x =
blanchet@42542
   326
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   327
blanchet@42542
   328
fun unmangled_type s =
blanchet@42542
   329
  s |> suffix ")" |> raw_explode
blanchet@42542
   330
    |> Scan.finite Symbol.stopper
blanchet@42542
   331
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   332
                                                quote s)) parse_mangled_type))
blanchet@42542
   333
    |> fst
blanchet@42542
   334
blanchet@42561
   335
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   336
fun unmangled_const s =
blanchet@42542
   337
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   338
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   339
  end
blanchet@42542
   340
blanchet@42994
   341
fun introduce_proxies format type_sys tm =
blanchet@42568
   342
  let
blanchet@42963
   343
    fun aux ary top_level (CombApp (tm1, tm2)) =
blanchet@42963
   344
        CombApp (aux (ary + 1) top_level tm1, aux 0 false tm2)
blanchet@42963
   345
      | aux ary top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   346
        (case proxify_const s of
blanchet@42568
   347
           SOME proxy_base =>
blanchet@42963
   348
           (* Proxies are not needed in THF, except for partially applied
blanchet@42963
   349
              equality since THF does not provide any syntax for it. *)
blanchet@42963
   350
           if top_level orelse
blanchet@42994
   351
              (is_setting_higher_order format type_sys andalso
blanchet@42994
   352
               (s <> "equal" orelse ary = 2)) then
blanchet@42568
   353
             (case s of
blanchet@42568
   354
                "c_False" => (tptp_false, s')
blanchet@42568
   355
              | "c_True" => (tptp_true, s')
blanchet@42568
   356
              | _ => name, [])
blanchet@42569
   357
           else
blanchet@42574
   358
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   359
          | NONE => (name, T_args))
blanchet@42574
   360
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42963
   361
      | aux _ _ tm = tm
blanchet@42963
   362
  in aux 0 true tm end
blanchet@42568
   363
blanchet@42994
   364
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   365
  let
blanchet@42568
   366
    fun do_term bs t atomic_types =
blanchet@41140
   367
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   368
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   369
      ||> union (op =) atomic_types
blanchet@38282
   370
    fun do_quant bs q s T t' =
blanchet@38518
   371
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   372
        do_formula ((s, T) :: bs) t'
blanchet@42562
   373
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   374
      end
blanchet@38282
   375
    and do_conn bs c t1 t2 =
blanchet@38282
   376
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   377
      #>> uncurry (mk_aconn c)
blanchet@38282
   378
    and do_formula bs t =
blanchet@38282
   379
      case t of
blanchet@42531
   380
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   381
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   382
        do_quant bs AForall s T t'
blanchet@38282
   383
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   384
        do_quant bs AExists s T t'
haftmann@38795
   385
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   386
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   387
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   388
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   389
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   390
      | _ => do_term bs t
blanchet@38282
   391
  in do_formula [] end
blanchet@38282
   392
blanchet@42750
   393
fun presimplify_term ctxt =
blanchet@42750
   394
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   395
  #> Meson.presimplify ctxt
blanchet@42750
   396
  #> prop_of
blanchet@38282
   397
wenzelm@41491
   398
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   399
fun conceal_bounds Ts t =
blanchet@38282
   400
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   401
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   402
fun reveal_bounds Ts =
blanchet@38282
   403
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   404
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   405
blanchet@42747
   406
fun extensionalize_term ctxt t =
blanchet@42747
   407
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   408
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   409
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   410
  end
blanchet@38608
   411
blanchet@38282
   412
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   413
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   414
    if Meson.is_fol_term thy t then
blanchet@38491
   415
      t
blanchet@38491
   416
    else
blanchet@38491
   417
      let
blanchet@38491
   418
        fun aux Ts t =
blanchet@38491
   419
          case t of
blanchet@38491
   420
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   421
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   422
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   423
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   424
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   425
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   426
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   427
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   428
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   429
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   430
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   431
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   432
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   433
              $ t1 $ t2 =>
blanchet@38491
   434
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   435
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   436
                   t
blanchet@38491
   437
                 else
blanchet@38491
   438
                   t |> conceal_bounds Ts
blanchet@38491
   439
                     |> Envir.eta_contract
blanchet@38491
   440
                     |> cterm_of thy
blanchet@39890
   441
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   442
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   443
                     |> reveal_bounds Ts
blanchet@39370
   444
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   445
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   446
      handle THM _ =>
blanchet@38491
   447
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   448
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   449
             else HOLogic.true_const
blanchet@38491
   450
  end
blanchet@38282
   451
blanchet@38282
   452
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   453
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   454
fun freeze_term t =
blanchet@38282
   455
  let
blanchet@38282
   456
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   457
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   458
      | aux (Var ((s, i), T)) =
blanchet@38282
   459
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   460
      | aux t = t
blanchet@38282
   461
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   462
blanchet@40204
   463
(* making fact and conjecture formulas *)
blanchet@42994
   464
fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
blanchet@38282
   465
  let
wenzelm@42361
   466
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   467
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   468
              |> transform_elim_prop
blanchet@41211
   469
              |> Object_Logic.atomize_term thy
blanchet@42563
   470
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   471
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@42742
   472
              |> Raw_Simplifier.rewrite_term thy
blanchet@42742
   473
                     (Meson.unfold_set_const_simps ctxt) []
blanchet@42747
   474
              |> extensionalize_term ctxt
blanchet@42750
   475
              |> presimp ? presimplify_term ctxt
blanchet@38282
   476
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   477
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   478
              |> kind <> Axiom ? freeze_term
blanchet@42962
   479
    val (combformula, atomic_types) =
blanchet@42994
   480
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   481
  in
blanchet@42640
   482
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   483
     atomic_types = atomic_types}
blanchet@38282
   484
  end
blanchet@38282
   485
blanchet@42994
   486
fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
blanchet@42994
   487
              ((name, loc), t) =
blanchet@42962
   488
  case (keep_trivial,
blanchet@42994
   489
        make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   490
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   491
    NONE
blanchet@41990
   492
  | (_, formula) => SOME formula
blanchet@42561
   493
blanchet@42994
   494
fun make_conjecture ctxt format prem_kind type_sys ts =
blanchet@38613
   495
  let val last = length ts - 1 in
blanchet@42709
   496
    map2 (fn j => fn t =>
blanchet@42709
   497
             let
blanchet@42709
   498
               val (kind, maybe_negate) =
blanchet@42709
   499
                 if j = last then
blanchet@42709
   500
                   (Conjecture, I)
blanchet@42709
   501
                 else
blanchet@42709
   502
                   (prem_kind,
blanchet@42709
   503
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   504
                    else I)
blanchet@42709
   505
              in
blanchet@42994
   506
                t |> make_formula ctxt format type_sys true true
blanchet@42994
   507
                                  (string_of_int j) General kind
blanchet@42962
   508
                  |> maybe_negate
blanchet@42709
   509
              end)
blanchet@38613
   510
         (0 upto last) ts
blanchet@38613
   511
  end
blanchet@38282
   512
blanchet@42682
   513
(** Finite and infinite type inference **)
blanchet@42682
   514
blanchet@42886
   515
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   516
  | deep_freeze_atyp T = T
blanchet@42886
   517
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   518
blanchet@42886
   519
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@42886
   520
blanchet@42682
   521
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   522
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   523
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   524
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   525
blanchet@42886
   526
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   527
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   528
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   529
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   530
  | should_encode_type _ _ _ _ = false
blanchet@42682
   531
blanchet@42837
   532
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   533
                             should_predicate_on_var T =
blanchet@42878
   534
    (heaviness = Heavy orelse should_predicate_on_var ()) andalso
blanchet@42878
   535
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   536
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   537
blanchet@42836
   538
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   539
    String.isPrefix bound_var_prefix s
blanchet@42836
   540
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   541
  | is_var_or_bound_var _ = false
blanchet@42836
   542
blanchet@42829
   543
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
   544
blanchet@42829
   545
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
   546
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
   547
    (case heaviness of
blanchet@42837
   548
       Heavy => should_encode_type ctxt nonmono_Ts level T
blanchet@42837
   549
     | Light =>
blanchet@42836
   550
       case (site, is_var_or_bound_var u) of
blanchet@42836
   551
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
   552
       | _ => false)
blanchet@42829
   553
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
   554
blanchet@42994
   555
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
   556
  let
blanchet@42994
   557
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
   558
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
   559
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
   560
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
   561
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
   562
  in homo end
blanchet@42682
   563
blanchet@42573
   564
(** "hBOOL" and "hAPP" **)
blanchet@41313
   565
blanchet@42574
   566
type sym_info =
blanchet@42563
   567
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   568
blanchet@42574
   569
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   570
  let
blanchet@42558
   571
    fun aux top_level tm =
blanchet@42558
   572
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   573
        (case head of
blanchet@42563
   574
           CombConst ((s, _), T, _) =>
blanchet@42558
   575
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   576
             I
blanchet@42558
   577
           else
blanchet@42563
   578
             let val ary = length args in
blanchet@42558
   579
               Symtab.map_default
blanchet@42558
   580
                   (s, {pred_sym = true,
blanchet@42563
   581
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   582
                        max_ary = 0, typ = SOME T})
blanchet@42563
   583
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   584
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   585
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   586
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   587
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   588
            end
blanchet@42558
   589
         | _ => I)
blanchet@42558
   590
        #> fold (aux false) args
blanchet@42558
   591
      end
blanchet@42558
   592
  in aux true end
blanchet@42674
   593
fun add_fact_syms_to_table explicit_apply =
blanchet@42834
   594
  fact_lift (formula_fold NONE (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   595
blanchet@42675
   596
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   597
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42966
   598
   (make_fixed_const predicator_name,
blanchet@42563
   599
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   600
  ([tptp_false, tptp_true]
blanchet@42563
   601
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   602
blanchet@42544
   603
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   604
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   605
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   606
blanchet@42558
   607
fun min_arity_of sym_tab s =
blanchet@42558
   608
  case Symtab.lookup sym_tab s of
blanchet@42574
   609
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   610
  | NONE =>
blanchet@42558
   611
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   612
      SOME s =>
blanchet@42570
   613
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
   614
        if s = predicator_name then 1
blanchet@42966
   615
        else if s = app_op_name then 2
blanchet@42966
   616
        else if s = type_pred_name then 1
blanchet@42557
   617
        else 0
blanchet@42547
   618
      end
blanchet@42544
   619
    | NONE => 0
blanchet@38282
   620
blanchet@38282
   621
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   622
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   623
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   624
   arguments and is used as a predicate. *)
blanchet@42558
   625
fun is_pred_sym sym_tab s =
blanchet@42558
   626
  case Symtab.lookup sym_tab s of
blanchet@42574
   627
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   628
    pred_sym andalso min_ary = max_ary
blanchet@42558
   629
  | NONE => false
blanchet@38282
   630
blanchet@42568
   631
val predicator_combconst =
blanchet@42966
   632
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
   633
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   634
blanchet@42568
   635
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   636
  case strip_combterm_comb tm of
blanchet@42542
   637
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   638
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   639
  | _ => predicator tm
blanchet@42542
   640
blanchet@42544
   641
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   642
blanchet@42544
   643
fun explicit_app arg head =
blanchet@42544
   644
  let
blanchet@42562
   645
    val head_T = combtyp_of head
blanchet@42693
   646
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   647
    val explicit_app =
blanchet@42966
   648
      CombConst (`make_fixed_const app_op_name, head_T --> head_T,
blanchet@42693
   649
                 [arg_T, res_T])
blanchet@42544
   650
  in list_app explicit_app [head, arg] end
blanchet@42544
   651
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   652
blanchet@42565
   653
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   654
  let
blanchet@42544
   655
    fun aux tm =
blanchet@42544
   656
      case strip_combterm_comb tm of
blanchet@42544
   657
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   658
        args |> map aux
blanchet@42557
   659
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   660
             |>> list_app head
blanchet@42544
   661
             |-> list_explicit_app
blanchet@42544
   662
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   663
  in aux end
blanchet@38282
   664
blanchet@42753
   665
fun chop_fun 0 T = ([], T)
blanchet@42753
   666
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
   667
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
   668
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
   669
blanchet@42780
   670
fun filter_type_args _ _ _ [] = []
blanchet@42780
   671
  | filter_type_args thy s arity T_args =
blanchet@42834
   672
    let
blanchet@42834
   673
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
   674
      val U = if s = app_op_name then
blanchet@42834
   675
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
   676
              else
blanchet@42834
   677
                s |> Sign.the_const_type thy
blanchet@42834
   678
    in
blanchet@42781
   679
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
   680
        [] => []
blanchet@42781
   681
      | res_U_vars =>
blanchet@42781
   682
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
   683
          U_args ~~ T_args
blanchet@42781
   684
          |> map_filter (fn (U, T) =>
blanchet@42781
   685
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
   686
                              SOME T
blanchet@42781
   687
                            else
blanchet@42781
   688
                              NONE)
blanchet@42781
   689
        end
blanchet@42780
   690
    end
blanchet@42780
   691
    handle TYPE _ => T_args
blanchet@42753
   692
blanchet@42994
   693
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
   694
  let
blanchet@42753
   695
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
   696
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
   697
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
   698
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
   699
        let
blanchet@42701
   700
          val level = level_of_type_sys type_sys
blanchet@42701
   701
          val (T, T_args) =
blanchet@42701
   702
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
   703
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
   704
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
   705
               since it leads to too many unsound proofs. *)
blanchet@42966
   706
            if s = const_prefix ^ app_op_name andalso
blanchet@42726
   707
               length T_args = 2 andalso
blanchet@42836
   708
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@42837
   709
               heaviness_of_type_sys type_sys = Heavy then
blanchet@42994
   710
              T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
blanchet@42701
   711
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
   712
                                    (T --> T, tl Ts)
blanchet@42701
   713
                                  end)
blanchet@42701
   714
            else
blanchet@42701
   715
              (T, T_args)
blanchet@42701
   716
        in
blanchet@42701
   717
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
   718
             NONE => (name, T_args)
blanchet@42701
   719
           | SOME s'' =>
blanchet@42753
   720
             let
blanchet@42753
   721
               val s'' = invert_const s''
blanchet@42831
   722
               fun filtered_T_args false = T_args
blanchet@42831
   723
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
   724
             in
blanchet@42701
   725
               case type_arg_policy type_sys s'' of
blanchet@42831
   726
                 Explicit_Type_Args drop_args =>
blanchet@42831
   727
                 (name, filtered_T_args drop_args)
blanchet@42831
   728
               | Mangled_Type_Args drop_args =>
blanchet@42994
   729
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
   730
               | No_Type_Args => (name, [])
blanchet@42701
   731
             end)
blanchet@42701
   732
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
   733
        end
blanchet@42753
   734
      | aux _ tm = tm
blanchet@42753
   735
  in aux 0 end
blanchet@42573
   736
blanchet@42962
   737
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42994
   738
  not (is_setting_higher_order format type_sys)
blanchet@42994
   739
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
   740
     #> introduce_predicators_in_combterm sym_tab)
blanchet@42994
   741
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   742
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42701
   743
  update_combformula (formula_map
blanchet@42962
   744
      (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
blanchet@42573
   745
blanchet@42573
   746
(** Helper facts **)
blanchet@42573
   747
blanchet@42573
   748
fun ti_ti_helper_fact () =
blanchet@42573
   749
  let
blanchet@42573
   750
    fun var s = ATerm (`I s, [])
blanchet@42589
   751
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   752
  in
blanchet@42612
   753
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   754
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
   755
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
   756
  end
blanchet@42573
   757
blanchet@42962
   758
fun helper_facts_for_sym ctxt format type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   759
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   760
    SOME mangled_s =>
blanchet@42573
   761
    let
blanchet@42573
   762
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   763
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
   764
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
   765
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
   766
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
   767
           else untyped_helper_suffix),
blanchet@42881
   768
          General),
blanchet@42573
   769
         let val t = th |> prop_of in
blanchet@42753
   770
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
   771
                    Mangled_Type_Args _ => true
blanchet@42753
   772
                  | _ => false) andalso
blanchet@42573
   773
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   774
                ? (case typ of
blanchet@42573
   775
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   776
                   | NONE => I)
blanchet@42573
   777
         end)
blanchet@42573
   778
      fun make_facts eq_as_iff =
blanchet@42994
   779
        map_filter (make_fact ctxt format type_sys false eq_as_iff false)
blanchet@42893
   780
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
   781
    in
blanchet@42573
   782
      metis_helpers
blanchet@42894
   783
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
   784
                  if metis_s <> unmangled_s orelse
blanchet@42894
   785
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
   786
                    []
blanchet@42573
   787
                  else
blanchet@42573
   788
                    ths ~~ (1 upto length ths)
blanchet@42893
   789
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
   790
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
   791
    end
blanchet@42573
   792
  | NONE => []
blanchet@42962
   793
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
   794
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
   795
                  []
blanchet@42573
   796
blanchet@42994
   797
fun translate_atp_fact ctxt format type_sys keep_trivial =
blanchet@42994
   798
  `(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
blanchet@42573
   799
blanchet@42962
   800
fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
blanchet@42962
   801
                       rich_facts =
blanchet@42573
   802
  let
blanchet@42573
   803
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   804
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   805
    val (facts, fact_names) =
blanchet@42573
   806
      rich_facts
blanchet@42573
   807
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   808
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   809
      |> ListPair.unzip
blanchet@42573
   810
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   811
       boost an ATP's performance (for some reason). *)
blanchet@42573
   812
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   813
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   814
    val all_ts = goal_t :: fact_ts
blanchet@42573
   815
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   816
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   817
    val tycons = type_consts_of_terms thy all_ts
blanchet@42994
   818
    val conjs =
blanchet@42994
   819
      hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
blanchet@42573
   820
    val (supers', arity_clauses) =
blanchet@42589
   821
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   822
      else make_arity_clauses thy tycons supers
blanchet@42573
   823
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   824
  in
blanchet@42573
   825
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   826
  end
blanchet@42573
   827
blanchet@42573
   828
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   829
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   830
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   831
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   832
blanchet@42573
   833
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   834
blanchet@42994
   835
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@42966
   836
  CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
blanchet@42994
   837
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
   838
           tm)
blanchet@42573
   839
blanchet@42878
   840
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
   841
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@42878
   842
    accum orelse (s = "equal" andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
   843
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
   844
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
   845
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
   846
blanchet@42994
   847
fun mk_const_aterm x T_args args =
blanchet@42994
   848
  ATerm (x, map (fo_term_from_typ false) T_args @ args)
blanchet@42994
   849
blanchet@42962
   850
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
blanchet@42829
   851
  CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42994
   852
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
   853
  |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42829
   854
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
   855
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
   856
  let
blanchet@42962
   857
    fun aux site u =
blanchet@42962
   858
      let
blanchet@42962
   859
        val (head, args) = strip_combterm_comb u
blanchet@42962
   860
        val (x as (s, _), T_args) =
blanchet@42962
   861
          case head of
blanchet@42962
   862
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
   863
          | CombVar (name, _) => (name, [])
blanchet@42962
   864
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42962
   865
        val arg_site = if site = Top_Level andalso s = "equal" then Eq_Arg
blanchet@42962
   866
                       else Elsewhere
blanchet@42994
   867
        val t = mk_const_aterm x T_args (map (aux arg_site) args)
blanchet@42962
   868
        val T = combtyp_of u
blanchet@42962
   869
      in
blanchet@42962
   870
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42962
   871
                tag_with_type ctxt format nonmono_Ts type_sys T
blanchet@42962
   872
              else
blanchet@42962
   873
                I)
blanchet@42962
   874
      end
blanchet@42962
   875
  in aux end
blanchet@42962
   876
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
   877
                             should_predicate_on_var =
blanchet@42829
   878
  let
blanchet@42994
   879
    val higher_order = is_setting_higher_order format type_sys
blanchet@42962
   880
    val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42573
   881
    val do_bound_type =
blanchet@42682
   882
      case type_sys of
blanchet@42722
   883
        Simple_Types level =>
blanchet@42994
   884
        homogenized_type ctxt nonmono_Ts level 0
blanchet@42994
   885
        #> mangled_type higher_order false 0 #> SOME
blanchet@42682
   886
      | _ => K NONE
blanchet@42878
   887
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
   888
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
   889
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
   890
        CombVar (name, T)
blanchet@42994
   891
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
   892
        |> do_term |> AAtom |> SOME
blanchet@42573
   893
      else
blanchet@42573
   894
        NONE
blanchet@42878
   895
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
   896
        let
blanchet@42878
   897
          val phi = phi |> do_formula pos
blanchet@42878
   898
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
   899
        in
blanchet@42834
   900
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
   901
                                        | SOME T => do_bound_type T)),
blanchet@42834
   902
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
   903
                      (map_filter
blanchet@42834
   904
                           (fn (_, NONE) => NONE
blanchet@42834
   905
                             | (s, SOME T) =>
blanchet@42878
   906
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
   907
                           xs)
blanchet@42834
   908
                      phi)
blanchet@42834
   909
        end
blanchet@42878
   910
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
   911
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
   912
  in do_formula o SOME end
blanchet@42573
   913
blanchet@42956
   914
fun bound_atomic_types format type_sys Ts =
blanchet@42727
   915
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42956
   916
                (atp_type_literals_for_types format type_sys Axiom Ts))
blanchet@42727
   917
blanchet@42956
   918
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
   919
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
   920
  combformula
blanchet@42727
   921
  |> close_combformula_universally
blanchet@42962
   922
  |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
   923
                              is_var_nonmonotonic_in_formula true
blanchet@42956
   924
  |> bound_atomic_types format type_sys atomic_types
blanchet@42573
   925
  |> close_formula_universally
blanchet@42573
   926
blanchet@42573
   927
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   928
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   929
   the remote provers might care. *)
blanchet@42956
   930
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
   931
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   932
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   933
                     else string_of_int j ^ "_") ^
blanchet@42647
   934
           ascii_of name,
blanchet@42956
   935
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
   936
           case locality of
blanchet@42879
   937
             Intro => intro_info
blanchet@42879
   938
           | Elim => elim_info
blanchet@42879
   939
           | Simp => simp_info
blanchet@42879
   940
           | _ => NONE)
blanchet@42573
   941
blanchet@42939
   942
fun formula_line_for_class_rel_clause
blanchet@42939
   943
        (ClassRelClause {name, subclass, superclass, ...}) =
blanchet@42573
   944
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   945
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   946
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   947
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
   948
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
   949
  end
blanchet@42573
   950
blanchet@42573
   951
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   952
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   953
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   954
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   955
blanchet@42939
   956
fun formula_line_for_arity_clause
blanchet@42939
   957
        (ArityClause {name, prem_lits, concl_lits, ...}) =
blanchet@42577
   958
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   959
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
   960
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
   961
                    (formula_from_fo_literal
blanchet@42895
   962
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
   963
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
   964
blanchet@42962
   965
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@42573
   966
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   967
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
   968
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42939
   969
               is_var_nonmonotonic_in_formula false
blanchet@42939
   970
               (close_combformula_universally combformula)
blanchet@42573
   971
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   972
blanchet@42956
   973
fun free_type_literals format type_sys
blanchet@42956
   974
                       ({atomic_types, ...} : translated_formula) =
blanchet@42956
   975
  atomic_types |> atp_type_literals_for_types format type_sys Conjecture
blanchet@42573
   976
               |> map fo_literal_from_type_literal
blanchet@42573
   977
blanchet@42573
   978
fun formula_line_for_free_type j lit =
blanchet@42577
   979
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   980
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42956
   981
fun formula_lines_for_free_types format type_sys facts =
blanchet@42573
   982
  let
blanchet@42956
   983
    val litss = map (free_type_literals format type_sys) facts
blanchet@42573
   984
    val lits = fold (union (op =)) litss []
blanchet@42573
   985
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   986
blanchet@42573
   987
(** Symbol declarations **)
blanchet@42544
   988
blanchet@42886
   989
fun insert_type ctxt get_T x xs =
blanchet@42677
   990
  let val T = get_T x in
blanchet@42886
   991
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@42886
   992
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@42677
   993
  end
blanchet@42677
   994
blanchet@42574
   995
fun should_declare_sym type_sys pred_sym s =
blanchet@42998
   996
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@42894
   997
  (case type_sys of
blanchet@42894
   998
     Simple_Types _ => true
blanchet@42894
   999
   | Tags (_, _, Light) => true
blanchet@42894
  1000
   | _ => not pred_sym)
blanchet@38282
  1001
blanchet@42886
  1002
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1003
  let
blanchet@42698
  1004
    fun add_combterm in_conj tm =
blanchet@42574
  1005
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1006
        (case head of
blanchet@42574
  1007
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1008
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1009
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1010
               Symtab.map_default (s, [])
blanchet@42886
  1011
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1012
                                         in_conj))
blanchet@42574
  1013
             else
blanchet@42574
  1014
               I
blanchet@42574
  1015
           end
blanchet@42574
  1016
         | _ => I)
blanchet@42698
  1017
        #> fold (add_combterm in_conj) args
blanchet@42574
  1018
      end
blanchet@42698
  1019
    fun add_fact in_conj =
blanchet@42834
  1020
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1021
  in
blanchet@42698
  1022
    Symtab.empty
blanchet@42698
  1023
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1024
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1025
  end
blanchet@42533
  1026
blanchet@42886
  1027
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
  1028
   models and hence that any types with these type classes is monotonic. *)
blanchet@42886
  1029
val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
blanchet@42886
  1030
blanchet@42685
  1031
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1032
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1033
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1034
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@42680
  1035
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
  1036
                  tm2)) =
blanchet@42680
  1037
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1038
     (case level of
blanchet@42886
  1039
        Nonmonotonic_Types =>
blanchet@42886
  1040
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1041
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1042
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1043
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1044
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1045
                                            : translated_formula) =
blanchet@42834
  1046
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1047
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1048
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1049
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1050
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1051
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1052
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1053
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1054
            nonmonotonic types not being empty. *)
blanchet@42886
  1055
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1056
    else
blanchet@42886
  1057
      []
blanchet@42829
  1058
  end
blanchet@42677
  1059
blanchet@42994
  1060
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1061
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1062
  let
blanchet@42994
  1063
    val (higher_order, T_arg_Ts, level) =
blanchet@42994
  1064
      case type_sys of
blanchet@42994
  1065
        Simple_Types level => (format = THF, [], level)
blanchet@42994
  1066
      | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1067
  in
blanchet@42998
  1068
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1069
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@42994
  1070
          |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1071
  end
blanchet@42579
  1072
blanchet@42592
  1073
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1074
blanchet@42956
  1075
fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1076
                                   n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1077
  let
blanchet@42709
  1078
    val (kind, maybe_negate) =
blanchet@42709
  1079
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1080
      else (Axiom, I)
blanchet@42753
  1081
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1082
    val bound_names =
blanchet@42579
  1083
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1084
    val bounds =
blanchet@42579
  1085
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1086
    val bound_Ts =
blanchet@42592
  1087
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1088
                             else NONE)
blanchet@42579
  1089
  in
blanchet@42998
  1090
    Formula (sym_formula_prefix ^ s ^
blanchet@42709
  1091
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1092
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1093
             |> fold (curry (CombApp o swap)) bounds
blanchet@42994
  1094
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42963
  1095
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42962
  1096
             |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1097
                                         (K (K (K (K true)))) true
blanchet@42956
  1098
             |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
blanchet@42709
  1099
             |> close_formula_universally
blanchet@42709
  1100
             |> maybe_negate,
blanchet@42879
  1101
             intro_info, NONE)
blanchet@42579
  1102
  end
blanchet@42579
  1103
blanchet@42956
  1104
fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42956
  1105
        n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1106
  let
blanchet@42829
  1107
    val ident_base =
blanchet@42998
  1108
      sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1109
    val (kind, maybe_negate) =
blanchet@42852
  1110
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1111
      else (Axiom, I)
blanchet@42829
  1112
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1113
    val bound_names =
blanchet@42829
  1114
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1115
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42994
  1116
    val cst = mk_const_aterm (s, s') T_args
blanchet@42830
  1117
    val atomic_Ts = atyps_of T
blanchet@42834
  1118
    fun eq tms =
blanchet@42834
  1119
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@42834
  1120
       else AAtom (ATerm (`I "equal", tms)))
blanchet@42956
  1121
      |> bound_atomic_types format type_sys atomic_Ts
blanchet@42830
  1122
      |> close_formula_universally
blanchet@42852
  1123
      |> maybe_negate
blanchet@42836
  1124
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42962
  1125
    val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
blanchet@42829
  1126
    val add_formula_for_res =
blanchet@42829
  1127
      if should_encode res_T then
blanchet@42852
  1128
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1129
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1130
                       simp_info, NONE))
blanchet@42829
  1131
      else
blanchet@42829
  1132
        I
blanchet@42829
  1133
    fun add_formula_for_arg k =
blanchet@42829
  1134
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1135
        if should_encode arg_T then
blanchet@42829
  1136
          case chop k bounds of
blanchet@42829
  1137
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1138
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1139
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1140
                               cst bounds],
blanchet@42879
  1141
                           simp_info, NONE))
blanchet@42829
  1142
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1143
        else
blanchet@42829
  1144
          I
blanchet@42829
  1145
      end
blanchet@42829
  1146
  in
blanchet@42834
  1147
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1148
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1149
  end
blanchet@42829
  1150
blanchet@42836
  1151
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1152
blanchet@42956
  1153
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1154
                                (s, decls) =
blanchet@42998
  1155
  case type_sys of
blanchet@42998
  1156
    Simple_Types _ =>
blanchet@42998
  1157
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42998
  1158
  | Preds _ =>
blanchet@42998
  1159
    let
blanchet@42998
  1160
      val decls =
blanchet@42998
  1161
        case decls of
blanchet@42998
  1162
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1163
          let val T = result_type_of_decl decl in
blanchet@42998
  1164
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1165
                       o result_type_of_decl) decls' then
blanchet@42998
  1166
              [decl]
blanchet@42998
  1167
            else
blanchet@42998
  1168
              decls
blanchet@42998
  1169
          end
blanchet@42998
  1170
        | _ => decls
blanchet@42998
  1171
      val n = length decls
blanchet@42998
  1172
      val decls =
blanchet@42998
  1173
        decls
blanchet@42998
  1174
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42998
  1175
                   o result_type_of_decl)
blanchet@42998
  1176
    in
blanchet@42998
  1177
      (0 upto length decls - 1, decls)
blanchet@42998
  1178
      |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1179
                                               nonmono_Ts type_sys n s)
blanchet@42998
  1180
    end
blanchet@42998
  1181
  | Tags (_, _, heaviness) =>
blanchet@42998
  1182
    (case heaviness of
blanchet@42998
  1183
       Heavy => []
blanchet@42998
  1184
     | Light =>
blanchet@42998
  1185
       let val n = length decls in
blanchet@42998
  1186
         (0 upto n - 1 ~~ decls)
blanchet@42998
  1187
         |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
blanchet@42998
  1188
                                                 nonmono_Ts type_sys n s)
blanchet@42998
  1189
       end)
blanchet@42579
  1190
blanchet@42956
  1191
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1192
                                     type_sys sym_decl_tab =
blanchet@42998
  1193
  sym_decl_tab
blanchet@42998
  1194
  |> Symtab.dest
blanchet@42998
  1195
  |> sort_wrt fst
blanchet@42998
  1196
  |> rpair []
blanchet@42998
  1197
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@42998
  1198
                                                     nonmono_Ts type_sys)
blanchet@42543
  1199
blanchet@42837
  1200
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
blanchet@42831
  1201
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1202
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1203
blanchet@42939
  1204
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1205
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1206
    if heading = needle then j
blanchet@42939
  1207
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1208
blanchet@42998
  1209
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1210
val explicit_declsN = "Explicit typings"
blanchet@41157
  1211
val factsN = "Relevant facts"
blanchet@41157
  1212
val class_relsN = "Class relationships"
blanchet@42543
  1213
val aritiesN = "Arities"
blanchet@41157
  1214
val helpersN = "Helper facts"
blanchet@41157
  1215
val conjsN = "Conjectures"
blanchet@41313
  1216
val free_typesN = "Type variables"
blanchet@41157
  1217
blanchet@42939
  1218
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@42939
  1219
                        explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1220
  let
blanchet@41313
  1221
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@42962
  1222
      translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
blanchet@42563
  1223
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42886
  1224
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42962
  1225
    val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
blanchet@42682
  1226
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1227
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1228
    val helpers =
blanchet@42962
  1229
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1230
                       |> map repair
blanchet@42894
  1231
    val lavish_nonmono_Ts =
blanchet@42894
  1232
      if null nonmono_Ts orelse
blanchet@42894
  1233
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1234
        nonmono_Ts
blanchet@42894
  1235
      else
blanchet@42894
  1236
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1237
    val sym_decl_lines =
blanchet@42731
  1238
      (conjs, helpers @ facts)
blanchet@42886
  1239
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1240
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1241
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1242
    val helper_lines =
blanchet@42956
  1243
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1244
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1245
                                    type_sys)
blanchet@42956
  1246
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1247
          else I)
blanchet@42522
  1248
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1249
       Flotter hack. *)
blanchet@38282
  1250
    val problem =
blanchet@42998
  1251
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1252
       (factsN,
blanchet@42956
  1253
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1254
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1255
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1256
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1257
       (helpersN, helper_lines),
blanchet@42962
  1258
       (conjsN,
blanchet@42962
  1259
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1260
            conjs),
blanchet@42956
  1261
       (free_typesN,
blanchet@42956
  1262
        formula_lines_for_free_types format type_sys (facts @ conjs))]
blanchet@42543
  1263
    val problem =
blanchet@42561
  1264
      problem
blanchet@42998
  1265
      |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
blanchet@42998
  1266
      |> (if is_format_typed format then
blanchet@42998
  1267
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1268
                                                   implicit_declsN
blanchet@42998
  1269
          else
blanchet@42998
  1270
            I)
blanchet@42646
  1271
    val (problem, pool) =
blanchet@42646
  1272
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@42881
  1273
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1274
    val typed_helpers =
blanchet@42881
  1275
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1276
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1277
                     else NONE)
blanchet@42881
  1278
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1279
                  ~~ helpers)
blanchet@42778
  1280
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1281
      if min_ary > 0 then
blanchet@42755
  1282
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1283
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1284
        | NONE => I
blanchet@42755
  1285
      else
blanchet@42755
  1286
        I
blanchet@38282
  1287
  in
blanchet@38282
  1288
    (problem,
blanchet@38282
  1289
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1290
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1291
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1292
     fact_names |> Vector.fromList,
blanchet@42881
  1293
     typed_helpers,
blanchet@42755
  1294
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1295
  end
blanchet@38282
  1296
blanchet@41313
  1297
(* FUDGE *)
blanchet@41313
  1298
val conj_weight = 0.0
blanchet@41770
  1299
val hyp_weight = 0.1
blanchet@41770
  1300
val fact_min_weight = 0.2
blanchet@41313
  1301
val fact_max_weight = 1.0
blanchet@42608
  1302
val type_info_default_weight = 0.8
blanchet@41313
  1303
blanchet@41313
  1304
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42998
  1305
  is_tptp_user_symbol s ? Symtab.default (s, weight)
blanchet@41313
  1306
  #> fold (add_term_weights weight) tms
blanchet@42577
  1307
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1308
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1309
  | add_problem_line_weights _ _ = I
blanchet@41313
  1310
blanchet@41313
  1311
fun add_conjectures_weights [] = I
blanchet@41313
  1312
  | add_conjectures_weights conjs =
blanchet@41313
  1313
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1314
      add_problem_line_weights conj_weight conj
blanchet@41313
  1315
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1316
    end
blanchet@41313
  1317
blanchet@41313
  1318
fun add_facts_weights facts =
blanchet@41313
  1319
  let
blanchet@41313
  1320
    val num_facts = length facts
blanchet@41313
  1321
    fun weight_of j =
blanchet@41313
  1322
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1323
                        / Real.fromInt num_facts
blanchet@41313
  1324
  in
blanchet@41313
  1325
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1326
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1327
  end
blanchet@41313
  1328
blanchet@41313
  1329
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1330
fun atp_problem_weights problem =
blanchet@42608
  1331
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1332
    Symtab.empty
blanchet@42608
  1333
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1334
    |> add_facts_weights (get factsN)
blanchet@42608
  1335
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  1336
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  1337
    |> Symtab.dest
blanchet@42608
  1338
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1339
  end
blanchet@41313
  1340
blanchet@38282
  1341
end;